Recent content by Topologist

@jgm40 Opportunity is something you create. For example, no-one ever told me to do mathematics when I was young. However, I did have several mathematics book in my house, mostly of my parents, on topics in mathematics such as abstract algebra, topology, analysis etc. I picked them up, started...

I am merely speculating here, of course, but judging from the names of the courses that he said he has taken, I suspect that they would be based on self-study. Even at Harvard, it is rare for faculty to offer such courses. Perhaps he is doing some kind of reading based course, although I could...

You might find the following page interesting: http://www.math.harvard.edu/pamphlets/gradsch.html I quote: "Many schools look at your transcript to see evidence of substantial exposure to serious mathematics (e.g. some graduate level courses)." In this regard, you will probably have...

I do not think that you quite understand the meaning of the comments here. You are clearly a top mathematics student but it is important to realize that there are people equally as good as you and perhaps even some with better looking CV's than you. One cannot judge whether one mathematics...

I think that there are certain "extents" to which you can absorb the material in a mathematics textbook. For instance, on a scale of 1-10, I would say that someone who reads all the definitions, theorems and discussions in a given section of a textbook in a day, and can engage in a 30 minute...